remote sensing and modeling of energetic electron
TRANSCRIPT
Adv. Radio Sci., 13, 233–242, 2015
www.adv-radio-sci.net/13/233/2015/
doi:10.5194/ars-13-233-2015
© Author(s) 2015. CC Attribution 3.0 License.
Remote sensing and modeling of energetic electron precipitation
into the lower ionosphere using VLF/LF radio waves and field
aligned current data
E. D. Schmitter1,†
1University of Applied Sciences Osnabrueck, 49076 Osnabrueck, Germany†deceased, 25 March 2015
Correspondence to: M. Förster ([email protected])
Received: 1 November 2014 – Revised: 30 April 2015 – Accepted: 30 April 2015 – Published: 3 November 2015
Abstract. A model for the development of electron den-
sity height profiles based on space time distributed ioniza-
tion sources and reaction rates in the lower ionosphere is
described. Special attention is payed to the definition of an
auroral oval distribution function for energetic electron en-
ergy input into the lower ionosphere based on a Maxwellian
energy spectrum. The distribution function is controlled by
an activity parameter which is defined proportional to radio
signal amplitude disturbances of a VLF/LF transmitter. Ad-
justing the proportionality constant allows to model precipi-
tation caused VLF/LF signal disturbances using radio wave
propagation calculations and to scale the distribution func-
tion. Field aligned current (FAC) data from the new Swarm
satellite mission are used to constrain the spatial extent of
the distribution function. As an example electron precipita-
tion bursts during a moderate substorm on the 12 April 2014
(midnight–dawn) are modeled along the subauroral propaga-
tion path from the NFR/TFK transmitter (37.5 kHz, Iceland)
to a midlatitude site.
1 Introduction
The lower ionosphere (60–85 km height) is forced from
above by extreme UV, especially Lyman α, solar flare X-
rays and energetic particle precipitation (electrons & 30 keV,
protons & 4 MeV, lower energetic particles do not pene-
trate so deeply). Forcing from below takes place via tides,
gravity- and planetary waves, but also lightning electromag-
netic pulses and upward discharges (Fig. 1). Ionization by
particles not only directly enhances the local electron/ion
Figure 1. Forcing of the lower ionosphere/mesosphere and remote
sensing instrumentation.
density but also leads to the formation of HOx and NOx
molecules. The latter family is rather long living and by ver-
tical transport also reaches the stratosphere where it catalyt-
ically affects the ozone budget, especially in the polar re-
gion (Clilverd et al., 2007; Salmi et al., 2011). This is one
example of the strong coupling of the different ionospheric
and atmospheric layers. Very low frequency and low fre-
quency (VLF/LF) electromagnetic radiation from man made
transmitters (15–60 kHz), but also from lightning, propagates
mainly between ground and the lower ionosphere. The prop-
agation conditions are strongly affected by the conductivity
of the lower ionosphere which is proportional to the quo-
tient of the electron density and collision frequency height
profiles. Remote VLF/LF sensing therefore since decades
proves as an inexpensive and reliable way to assess forc-
ing processes in this layer, also with regard to auroral pre-
Published by Copernicus Publications on behalf of the URSI Landesausschuss in der Bundesrepublik Deutschland e.V.
234 E. D. Schmitter: Remote sensing and modeling of energetic electron precipitation
Figure 2. The monitored propagation path (red line; transmitter:
NRK, receiver: Rx). Also indicated: magnetometers LEIRV: Leir-
vogur, LER: Lerwick; riometers: ABI, SOD, OULU: Abisko, So-
dankyla, Oulu.
cipitation activity (Cummer et al., 1996, 1998). During the
last years we have developed a modeling scheme that al-
lows to assess ionospheric forcing parameters from VLF/LF
amplitude and phase recordings of distant Minimum Shift
Keying (MSK) transmitters (Schmitter, 2010, 2011, 2012,
2013, 2014). As the amplitude of these transmissions is con-
stant, any observed variations are caused along the propaga-
tion path. The monitored propagation path from the VLF/LF
transmitter with the call sign NRK/TFK (37.5 kHz, 63.9◦ N,
22.5◦W, Iceland) to our receiver site 52◦ N, 8◦ E (NW Ger-
many, 2210 km) starts in the subauroral domain and ex-
tends to midlatitudes (Fig. 2). In this paper we extend our
model to include forcing by energetic electrons. The pene-
tration depths of energetic electrons are shown in Fig. 3. As-
suming a Maxwellian electron energy distribution electrons
with a folding energy exceeding 30 keV have their ioniza-
tion maximum in the lower ionosphere (. 85 km) strongly
affecting VLF/LF propagation. Riometers monitor cosmic
noise absorption at about 90–100 km height and in this re-
spect they are also sensitive to electron precipitation, how-
ever with regard to lower energies (∼ 10 keV, i.e. auroral
electrons). Magnetometer recordings reflect the current vari-
ations caused by geomagnetic storm/substorm conditions
which often are accompanied by particle precipitation. Large
scale energetic electron precipitation modify the auroral elec-
trojet and lead to variations of the AL index. In this way
ground based observations by riometers and magnetometers
at proper sites yield important additional information with
regard to the identification of energetic electron precipitation
along the VLF/LF propagation path. The sources of the pre-
Figure 3. Ionization rate vs. height profile for Maxwellian elec-
trons of different folding energies E0 (normalized to the energy
flux rateQ0 = 1 mW m−2= 1 erg cm−2 s−1
= 10−7 J cm−2 s−1=
6.25 · 108 keV cm−2 s−1). Atmospheric model: COSPAR Interna-
tional Reference Atmosphere (CIRA86, June, 50◦ N).
cipitation are the radiation belts (Thorne, 1974; Carson et al.,
2012; Thorne et al., 2013). So, for a detailed characteriza-
tion of precipitation, satellite data are indispensable, even if
a specific domain (e.g. around the VLF/LF propagation path)
cannot be monitored continuously.
Mapping down electric and magnetic field measurements
and derived data (field aligned currents, FACs, Ritter et al.,
2013) from the Swarm satellites yields important information
for the assessment of the energy input into the ionosphere,
particularly with regard to the path and spatial extent of par-
ticle precipitation as well as the acceleration mechanisms.
At least a part of the energetic electron precipitation is cou-
pled to the midnight–dawn region 2 (equatorward) currents
and the dusk–midnight region 1 (poleward) currents (Ohtani
et al., 2010). So it may be expected, that the subauroral VLF
propagation path is mainly affected by energetic electron pre-
cipitation coupled to region 2 (equatorward) field aligned
currents, however compare the discussion of measured FAC
data with regard to this simple picture in Sect. 5. In this paper
we describe the VLF remote sensing procedure followed by
the discussion of our model for the calculation of the electron
density profiles, especially with regard to forcing events like
electron precipitation. After the description of the VLF radio
wave propagation calculations we discuss an example event:
electron precipitation bursts during a moderate substorm on
the 12 April 2014 (midnight–dawn) and the derivation of the
precipitation energy input along a VLF propagation path in
space and time from VLF data as well as using field aligned
current data from the new Swarm satellite mission (launch:
Adv. Radio Sci., 13, 233–242, 2015 www.adv-radio-sci.net/13/233/2015/
E. D. Schmitter: Remote sensing and modeling of energetic electron precipitation 235
22 November 2013). This mission was designed to measure
the magnetic signals from Earth’s core, mantle, crust, oceans,
ionosphere and magnetosphere. It consists of a constellation
of three identical satellites in low polar orbits: two of them
orbit side-by-side, descending from an initial altitude of 460–
300 km over 4 years; the third maintains an altitude of about
530 km. Each satellite carries a vector field magnetometer, an
absolute scalar magnetometer and an electric field instrument
(for a complete description see www.esa.int). In our paper the
field aligned current (FAC) data, a Level 2 product generated
from the magnetic field data, are used.
2 Remote sensing
Remote sensing of lower ionosphere conditions (bottomside
sounding) by monitoring low and very low frequency radio
signal propagation has been a well known method for several
decades. MSK (Minimum Shift Keying) transmitters prove
useful in this respect because of their constant amplitude
emissions. We have analyzed the signal amplitude and phase
variations of the NRK/TFK transmitter (37.5 kHz, 63.9◦ N,
22.5◦W, Iceland) received at a midlatitude site (52◦ N, 8◦ E)
with a great circle distance of 2210 km. The receiver has been
set up with a ferrite coil oriented for maximum signal ampli-
tude of the horizontal magnetic field. After preamplification a
stereo sound card computer interface with 192 kbit sampling
rate is used. The second channel is fed with the 1-s pulse
of a GPS receiver. Our software reads a 170 ms signal train
each second and extracts within the narrow MSK bandwidth
(200 Hz with NRK) amplitude and phase with regard to the
rising GPS-pulse flank yielding a time synchronization better
than 100 ns, corresponding to phase detection errors of 1.4◦
at 37.5 kHz. For the amplitude the signal to noise ratio (SNR)
is recorded. SNR= 0 dB is defined by the averaged signal
level received during transmitter maintenance drop outs. The
time stability of both transmitters proves to be sufficient for
continuous day and night monitoring not only of the ampli-
tude but also of the phase. Our phase detection algorithm for
MSK signals records phases between −90 and +90◦.
The NRK propagation path proceeds most of its way
through the subauroral domain to the midlatitude receiver
site and proves well suited to study lower ionosphere forc-
ing from above by particle precipitation (Schmitter, 2010)
and solar flares (Schmitter, 2013) as well as forcing from be-
low by planetary wave activity (Schmitter, 2011, 2012). In
this paper we concentrate on forcing by energetic electron
precipitation.
3 Modeling electron density profiles
A well known parametrization for the conductivity of the
lower ionosphere (about 60–95 km height) is the two param-
eter model of Wait and Spies (1964) with effective height h′
(km) and profile steepness β (1 / km):
σ(h)= σ0eβ(h−h′), (1)
with σ0 = σ(h= h′)= 2.22 · 10−6 S m−1.
From Eq. (1) together with the collision frequency profile
fc(h)= f0e−h/H , f0 = 1.816 · 1011 Hz and the relation be-
tween conductivity and electron density appropriate for the
very low frequency range σ = ε0ω2
p
fc=
e2ne
mefc(ωp: plasma fre-
quency) we get the classic Wait and Spies (1964) electron
density parametrization of the lower ionosphere:
ne = n0e−h/H eβ(h−h
′), (2)
with n0 = 1.43 · 1013 m−3 and scale height H = 1/0.15=
6.67 km corresponding to an isothermal atmosphere with
T = 230 K.
While this loglinear electron density–height relation often
is a reasonable first order approximation and intuitive with
regard to the interpretation of its two parameters, it does
not explain anything about the physical and chemical pro-
cesses generating the profiles. We therefore want to go a
step further in this respect and use reaction rate equations
describing the development of the density profiles of elec-
trons and ions. Chemical reaction based modeling has been
done in the past at various levels of specification. A very
detailed model of the complex D-layer chemistry is the So-
dankyla Ion Chemistry (SIC) model which takes into account
several hundred reactions and external forcing due to solar
radiation (1–422.5 nm wavelength) as well as particle pre-
cipitation (Verronen et al., 2002). Several approaches have
been made to reduce complexity to most relevant reaction
types – at the cost of introducing effective reaction parame-
ters lumping together different processes. For example: the
14− ion+ electron model of Torkar and Friedrich (1983);
the 6− ion+ electron Mitra–Rowe model (Mitra and Rowe,
1972; Mitra, 1975); the 3− ion+ electron Glukhov–Pasko–
Inan model (Glukhov et al., 1992); the electron “only” model
(Rodger et al., 1998, 2007).
With regard to VLF/LF remote sensing the electron den-
sity profiles are of main interest. For this reason and also to
keep the effort for the propagation calculations tolerable we
use an extended version of the electron “only” model. The
model is extended by taking into account electron detach-
ment reactions. They provide an additional electron source
which gains special importance around dusk and dawn, when
Lyman α radiation is weak. This leads to the following rate
equations for the electron-, positive ion- and negative ion
density distributions, ne, n−, n+ (m−3):
∂ne
∂t= q −αDn+ne−βnne+ (γn+ ρ)n−, (3)
∂n−
∂t=−αin+n−+βnne− (γn+ ρ)n−. (4)
www.adv-radio-sci.net/13/233/2015/ Adv. Radio Sci., 13, 233–242, 2015
236 E. D. Schmitter: Remote sensing and modeling of energetic electron precipitation
Average neutrality is assumed: n+ = ne+ n− and spatial
diffusion is neglected.
– q: ion-pair production (m−3 s−1), during daytime
caused by Lyman α radiation and solar X-rays (from
flares), during nighttime mainly by scattered Lyman
α radiation and cosmic rays. Particle precipitation can
cause additional ionization at any time. See the next
subsection for a detailed discussion.
– αD,i: electron (D) and negative ion (i) recombination co-
efficients (m3 s−1)
– βn: three body attachment coefficient (s−1)
– γn, ρ: coefficients for electron detachment from nega-
tive ions by collision with neutrals or by photons re-
spectively.
The reaction rates depend on the density of the reaction
partners, i.e. the pressure as well as the temperature T (below
100 km height we can assume local thermodynamic equilib-
rium: T = Tneutrals = Tions = Telectrons) . This, as well as rel-
ative abundances of ion species with different recombination
coefficients, means, that the reaction rates vary with height.
We use reaction rates as provided by Brekke (1997), with
the exception of the attachment coefficient βn, where we use
the more detailed relations provided in Rodger et al. (1998,
2007).
All numerical integrations are done using the classic
Runge-Kutta algorithm with variable time step size (0.1, . . .,
2 s).
We now describe the ionization processes in the lower
ionosphere which are included in our model.
3.1 Forcing processes characterizing undisturbed
conditions
Before considering disturbance events the processes gener-
ating the background ionization have to be modeled. In the
lower ionosphere we have continuous forcing from cosmic
radiation and solar Lyman α extreme UV:
– cosmic radiation: the ionization rate is proportional to
the neutral density nn absorbing the radiation:
qcosmic = c0nn, (5)
where c0 increases with geomagnetic latitude (1.2 ·
10−18. . .1.2 · 10−17 s−1 between 0 and 60◦ latitude)
(Nicolet and Aikin, 1960). With undisturbed conditions
cosmic radiation is the main forcing process below
80 km height during the night. During daytime this tran-
sition height drops to 65–70 km.
– solar Lyman α radiation (121.57 nm) on the day side
and night side via scattering:
The Lyman α photon energy of 10.2 eV is high enough
to ionize NO but not the major species O2, N2, so, with
ILα,∞ as the Lyman α intensity incident at the top of the
atmosphere:
qLα = σNO · nNO · ILα,∞e−τ . (6)
ILα,∞ varies with solar activity in the range 2.5, . . .,5 ·
1015 photons s−1 m−2. The optical depth integrated
along the ray path with O2 as the main absorbing species
is:
τ =
∫σO2· nO2
ds. (7)
With Nicolet and Aikin (1960) we use σNO = 2 ·
10−22 m2 for the ionization cross section of NO and
σO2= 10−24 m2 for the absorption cross section of O2
at 121.57 nm. nO2is 0.21 of the total number density
at mesospheric heights. nNO varies considerably: as the
measurements of the Halogen Occultation Experiment
(HALOE) of the Upper Atmosphere Research Satel-
lite (UARS) have shown, the NO number density be-
tween 60 and 90 km height at undisturbed conditions
during the same day can vary at least between 1011 and
1013 m−3 . We adopt 5 · 1012 m−3 as an average undis-
turbed value. The concentration of NO is significantly
enhanced during particle precipitation and for hours af-
terwards (Barth et al., 2001; Saetre et al., 2004) – which
has to be taken into account for the description of pre-
cipitation events during daylight.
3.2 Energetic electron precipitation
With regard to forcing processes leading to disturbed condi-
tions we focus on electron precipitation in this paper. Elec-
trons with energies & 30 keV (Fig. 3) and protons with en-
ergies & 4 MeV penetrate down into the lower ionosphere
(. 85) km. Proton precipitation are mostly confined to the
polar domain, which is not crossed by the propagation path
used in this investigation (Iceland – NW Germany). Different
approaches to predict the auroral oval were summarized by
Sigernes et al. (2011).
With Fang et al. (2008) we model the electron impact ion-
ization rate as
qprecip =Q0
f (E0,ρH)
21εH, (8)
with Q0 (keV cm−3 s−1): total vertically incident electron
flux at the top of the atmosphere.
The fractionf (E0,ρH)
21εHstands for the ionization efficiency
of an electron of (folding) energy E0 at a specific height and
temperature:
Adv. Radio Sci., 13, 233–242, 2015 www.adv-radio-sci.net/13/233/2015/
E. D. Schmitter: Remote sensing and modeling of energetic electron precipitation 237
ρ (g cm−3): atmospheric mass density, H = kTMg
the scale
height in cm at temperature T and with mean atmospheric
molecular mass M , and gravitational acceleration g (to ease
the comparison with literature we use keV and cm units
here).1ε = 35·10−3 keV: mean energy loss per ion pair pro-
duction, E0 (keV): the folding energy of a Maxwellian elec-
tron energy spectrum:
N(E)=Q0
2E30
Ee−E/E0 (9)
N(E) is the differential hemispherical electron number flux
(keV cm−2 s−1).
The numerical evaluation of the energy deposition func-
tion f (E0,ρH) is described in detail in Fang et al. (2008).
We model the incident electron flux Q0 (keV cm−2 s−1)
as a function of the local auroral activity a, geographic lati-
tude, longitude and universal time UT according to Schmitter
(2010):
Q0(a, lat, lon,UT)= c a w2e−
w
2σ2 , (10)
with c = 7.5 · 109 (keV cm−2 s−1). w is a dimensionless dis-
tance parameter with regard to the magnetic pole defined
as follows: with the projected coordinates x = r cos(long),
y = r sin(long), r = re cos(lat), re = 6371 km as compo-
nents of a vector rT = (x,y) we define the vector rn =
RUT(r−rmag pole) which centers the coordinates at the mag-
netic pole and rotates according to the universal time UT
using the usual 2 dimensional rotation matrix with UT ex-
pressed as rotation angle. w = rnT M rn is the bilinear form
of rn scaling these coordinates to an elliptic figure with semi
axes as = (1590+130a) km and bs = (1270+100a) km with
the scaling matrix M= (1/a2s 0;0 1/b2
s ). With this proce-
dure the auroral oval is fixed relative to the longitude of the
sun with the more intensive part at local midnight. As an ex-
ample of this type of distribution function see Fig. 4. Our
approach for modeling the auroral oval distribution can be
compared to that described in Semeniuk et al. (2008). They
use poleward and equatorward boundaries to parametrize the
auroral oval. Our formulation was inspired by the POES au-
roral oval data which made use of an auroral activity param-
eter (this product is replaced by the Ovation–Prime–model,
www.swpc.noaa.gov/models since 14 February 2014). In
contrast to the POES global (hemispheric) activity our activ-
ity parameter quantifies the local precipitation intensity Q0.
The constant c = 7.5 · 109 (keV cm−2 s−1) is defined such
that the elliptic shapes according to the NOAA POES sta-
tistical auroral activity maps (www.swpc.noaa.gov/pmap/)
are reproduced and by integrating Q0 over the hemispheric
area the total hemispheric power input P at auroral ac-
tivity index a = 0, . . .,10 results in accordance with the
NOAA POES data (www.swpc.noaa.gov/ftpdir/lists/hpi/). It
is roughly P = ea/2 GW (GigaWatt).
Figure 4. The auroral oval distribution function for 03:00 UT and
POES activity level 10. The two rings mark 60 and 80◦ geographic
latitude. The cross left from the North Pole (center of the rings) is
the magnetic south pole. Colorbar: erg cm−2 s−1=mW m−2. The
VLF propagation path from Iceland to NW Germany (2210 km dis-
tance) is also marked.
The local auroral activity a at time t is parametrized pro-
portional to the VLF/LF amplitude dip:
a(t)= cdB(ampundisturbed− ampdisturbed(t)) (11)
The proportionality constant is measured in auroral activ-
ity units per signal amplitude drop (dB).
3.3 Constraining the precipitation distribution
function using Swarm FAC data
Because the definition of the electron energy input distribu-
tion function Q0 is a main result of this paper we discuss it
in some more detail. For a better understanding we approxi-
mate the oval semi axes parameters as and bs by the circular
average γ = 1380+ 115a km and get
Q0∼= c a
(d
γ
)4
e−
(dγ
)2/2σ 2
, (12)
where d is the distance from the magnetic pole for the ge-
ographic point in question. At at dmax = 2γ σ the function
attains its maximum Q0(dmax)= c a(2σ)4/e2 (e = exp(1)).
The dimensionless width σ is parametrized by σ = σ0+
σ1a(1+ 0.25cos(φUT)) with φUT = 0 at local midnight.
Assuming that electron precipitation is confined to the
range of significant field aligned currents we constrain Q0
using Swarm FAC data, compare Figs. 5 and 6. Figure 5
shows the FAC distribution as recorded by the Swarm A,B,C
satellites during their orbits between 0:00 and 4:00 UT on 12
April 2014. Figure 6 shows the FACs along a nearly merid-
ional cut through the auroral oval at 5◦W longitude between
50 and 85◦ N latitude. Displayed in this figure are the results
www.adv-radio-sci.net/13/233/2015/ Adv. Radio Sci., 13, 233–242, 2015
238 E. D. Schmitter: Remote sensing and modeling of energetic electron precipitation
Figure 5. Field aligned currents from Swarm satellites A, B, C
on day 12 April 2014 from orbits between 1.9 and 4.5 h together
with the VLF propagation path Iceland-NW Germany. Underlying
(green) the auroral oval distribution function according to Fig. 4 is
shown.
from the satellites A and C which are flying side by side and
cross the indicated latitudes in about 12 min. Their separation
according to the specifications is 1.4◦ in geographic longi-
tudes corresponding to 78 km at 60◦ N. A time delay of max.
10 s along their orbit corresponds to max. 70 km distance in
latitude. At the time of preparation of this paper the com-
bined FAC data evaluation from both satellites was not avail-
able. The currents are significant between 61◦ N and 76◦ N
at a common longitude of ∼= 5◦W, which corresponds to a
local auroral oval width of 1800 km. On the average FACs
are negative in the equatorward half of the auroral oval and
positive on the poleward half (by definition the FACs are par-
allel to the magnetic field lines and point inwards at northern
latitudes). In detail however the 20 s low passed data exhibit
5 periods of different FAC domains across the auroral oval,
each of a width of about 360 km. With regard to the FAC
evaluation method see Ritter et al. (2013).
Now let dp,de be the distances from the magnetic pole
of the poleward and equatorward FAC limit points (76◦ N,
5◦W; 61◦ N, 5◦W) for the parallel overflight of Swarm
satellites A and C between 2.77 and 2.93 h on the day
12 April 2014. Requiring Q0(dp)=Q0(de)∼= 0 we numer-
ically find for an activity a = 10σ0 = 0.2 and σ1 = 0.02
as consistent parameters for the width σ = σ0+ σ1a(1+
0.25 cos(φUT)), UT= 2.85 h. For the resulting shape of the
Q0-function see Figs. 4 and 5. An investigation of other pre-
cipitation events is necessary to test the range of validity of
the parametrization of the electron input distribution func-
tion.
With all the ionization sources and reaction rates defined
by the rate equations (Eqs. 3 and 4) can be integrated. The
Figure 6. Field aligned currents from Swarm satellites A and C fly-
ing side by side, 12 April 2014, 2.8–2.9 h at about 5◦W longitude
(Atlantic, north of Scotland), 20 s low pass filtered. The data corre-
spond to the (A, C) orbits near the center of Fig. 5. This figure and
Fig. 5 are based on Swarm Level 2 data.
resulting electron density ne as function of time, height and
position along the radio wave propagation path is the essen-
tial input for the propagation calculation. The cdB parame-
ter, Eq. (11), is adjusted to yield the best possible fit of the
calculated signal amplitude to the disturbed recorded signal
amplitude.
4 Propagation calculations
For frequencies below the plasma frequency
√e2ne
ε0 methe
space between the conducting Earth ground and the iono-
sphere behaves like a leaky waveguide. For the VLF/LF
range the diffuse upper waveguide boundary is formed by the
lower ionosphere (60–90 km height). Propagation calculation
in our case is the task to calculate at a ground based receiver
position the signal field amplitude and phase of a ground
based transmitter (vertical electric and horizontal magnetic
field components). Besides transmitter radiated power and
antenna characteristics the essential input to the calculation
are the conductivities of the waveguide along the great cir-
cle propagation path. We use the LWPC (Long Wave Prop-
agation Capability) code (Ferguson, 1998) for this purpose.
It includes a world wide map of the ground conductivities.
For the ionospheric conductivity (σ = e2ne
mefc) the collision fre-
quency and electron density height profiles along the path
have to be provided. The collision frequency height profile
is usually assumed to be constant along the path: fc(h)=
f0e−h/H , f0 = 1.816 · 1011 Hz, H = 6.67 km. It may how-
Adv. Radio Sci., 13, 233–242, 2015 www.adv-radio-sci.net/13/233/2015/
E. D. Schmitter: Remote sensing and modeling of energetic electron precipitation 239
Figure 7. 12 April 2014: From top to bottom: Leirvogur magne-
tometer data (horizontal magnetic field component); energetic elec-
tron precipitation data from the mep0e1-sensors of 5 POES/Metop
satellites that had overflights at the time (UT hours) and within the
area indicated; recorded (blue) and modeled (red) VLF/LF ampli-
tude and phase data during pulsed electron precipitation along the
propagation path; electron kinetic energy input fluxQ0 (Eq. 10) be-
tween 0.7 and 3.7 h on 12 April 2014 derived from VLF propagation
modeling exemplary for two segments along the propagation path
(at the transmitter and half way to the receiver) using a Maxwellian
electron energy spectrum with a folding energy of 40 keV. The Leir-
vogur magnetometer and VLF/LF data display a zoomed part of
Fig. 8.
ever be modulated by gravity or planetary waves (Schmitter,
2012). The electron density ne(h) at height h changes along
the path with sun zenith angle, activity of the sun (e.g. so-
lar flares, Schmitter, 2013) and because of local forcing, e.g.
particle precipitation.
The propagation path is divided in 50 km segments. Each
segment is provided with the proper electron density height
profile (integrated from the rate equations, Sect. 3) for the
time step and the location in question. Propagation calcula-
tions are done in one minute intervals (however the integra-
tion of the rate equations yielding the electron density pro-
files has to use much smaller step sizes, typically 0.1–2 s).
LWPC then does a full wave calculation resulting in the
vertical electric field amplitude and phase at the receiver
site, the horizontal magnetic field data being directly propor-
tional. To allow comparisons with our recorded data ampli-
tude results are displayed in dB above the noise level, phases
in degree, compare Fig. 7, panels 3 and 4 from top.
5 Results
In Fig. 7 as an example we see the course of the VLF/LF
amplitude and phase (blue) during pulsed electron precipita-
tion (panels 3 and 4 from top, zoomed portion of Fig. 8, bot-
tom panel) together with our model calculation (red) where
the ionization by energetic electrons is accounted for by a
Maxwellian spectrum with 40 keV folding energy with im-
pact ionization parametrization from Fang et al. (2008) and
an intensity and space distribution according to the auroral
oval model function Q0, Eq. (10), which accounts for the
precipitation intensity distribution in space and time, as de-
scribed in Sects. 3.2 and 3.3. For comparison the energetic
electron (E > 30 keV) flux into the loss cone as observed by
the low orbit polar orbiters POES15,16,18,19 and Metop02
satellites during their overflights (panel 2 from top, mep0e1
data) and the Leirvogur magnetometer data (top panel) are
shown. Within 52–65◦ N latitude and −90 to +90◦ E longi-
tude encompassing the propagation path of the POES/Metop
satellite data confirm sporadically energetic electron precipi-
tation during the time of the VLF events (there was no en-
hanced proton level at that time). The magnetometer data
confirm a synchronous ionospheric current activity in the
vicinity of the NRK transmitter (Leirvogur is situated about
50 km NW of the NRK transmitter). In the non zoomed
Fig. 8, top panel, the difference to the undisturbed situation
is more clearly to be seen.
There are two parameters in the model that are fitted to
the data: the proportionality constant cdB (auroral activity per
signal amplitude drop (dB)) yielding the activity parameter
a(t)= cdB(ampundisturbed− ampdisturbed(t)), and the folding
energyE0 of the electron energy spectrum (40 keV in our ex-
ample case). cdB has been adjusted for best fit of the modeled
signal amplitude to the disturbed recorded signal amplitude.
Changing the folding energy by more than −5 or +10 keV
degenerates the fit quality significantly.
Level 2 data from the Swarm mission are used to iden-
tify the spatial extension of field aligned current densities
(FACs). With this information the precipitation boundaries
are assessed and the electron input distribution function Q0
has been constrained.
The FAC constrained spatial distribution of the precipita-
tion along the propagation path together with the VLF/LF
amplitude variations yields cdB = 0.2 (auroral activity units
per dB signal amplitude drop) at 37.5 kHz and supports the
www.adv-radio-sci.net/13/233/2015/ Adv. Radio Sci., 13, 233–242, 2015
240 E. D. Schmitter: Remote sensing and modeling of energetic electron precipitation
Figure 8. Days 11 and 12 of April 2014: effect of a series of energetic electron precipitation bursts with regard to VLF/LF signals. Lower
panel: VLF amplitude (dB SNR, red) and phase (deg, blue). The top panel displays the LEIRV magnetometer response reflecting ionospheric
current fluctuations during the substorm condition starting in the evening hours of 11 April 2014. (LEIRV: Leirvogur, Iceland, 50 km NW
of the NRK transmitter). The humps in the VLF/LF signal during daytime of 11 April 2014 are solar flare responses. Sunrise and sunset are
marked by vertical lines.
assumption of an E0 = 40 keV Maxwellian electron spec-
trum in the model calculations. cdB is expected to be constant
in our modeling scheme, so that after calibration an appli-
cation with regard to other electron precipitation events can
concentrate on the determination of E0, which can be a func-
tion of time.
As the main modeling result the energy input from elec-
tron precipitation as a function of time is available for each
of the 50 km segments along the VLF propagation path (Q0
distribution function). For two segments (near the transmit-
ter and half ways along the propagation path to the receiver)
the electron input energy flux results are shown in Fig. 7,
bottom panel. The maximum energy flux rate at the trans-
mitter coordinates 64◦ N 22.5◦W is 5 · 107 keV cm−2 s−1=
0.08 mW m−2. Half way to the receiver coordinates (58.8◦ N,
4.7◦W) the flux is reduced by two orders of magnitude.
The ionization rate vs. height characteristics for the reported
fluxes and E0 = 40 keV can be read from Fig. 3 (maximum:
8 · 108 m−3 s−1 at 78 km height).
The variation of theQ0 function (Fig. 7, bottom panel) re-
flects the course of the disturbed VLF/LF signal amplitude
because we define the activity parameter a(t) (which con-
trols the electron input) proportional to the signal amplitude,
Eq. (11). The constant cdB is chosen for a good fit of recorded
and modeled VLF/LF signal amplitude data. The modeled
phase also has to reflect the a(t) course (here in an inverted
way) because it is an input into the propagation calculation,
however there is only little correlation to the recorded phase.
This can be understood if we take into account that signal
phases in contrast to amplitudes are sensitive to all kinds of
effects along the propagation path in a cumulative way.
With regard to the spatial resolution of the derived flux val-
ues we recall that the main part of the electromagnetic energy
that is transferred from a transmitter to a receiver is contained
in the first Fresnel zone, an ellipsoid encompassing the prop-
agation path with an extension orthogonal to the propagation
path of the order of one wavelength (λ= 8 km for 37.5 kHz)
near the transmitter and the receiver and a maximum ex-
tension of 0.5√λd = 66 km at half way (Tx–Rx distance
d = 2210 km). So with a segment length of 50 km along the
propagation path the spatial resolution of our VLF/LF re-
mote sensing model, i.e. the averaging area, varies between
8 ·50 km2 near to the transmitter and near to the receiver and
66 · 50 km2 at half way.
6 Conclusions
The main objective of the work described in this paper is to
advance our VLF/LF propagation model by including the ef-
fect of electron particle precipitation. The extended model al-
lows for the characterization of Maxwellian electron energy
spectra along the VLF/LF propagation path by using data
from continuous VLF/LF remote sensing and field aligned
current density data from the new Swarm mission. The cur-
Adv. Radio Sci., 13, 233–242, 2015 www.adv-radio-sci.net/13/233/2015/
E. D. Schmitter: Remote sensing and modeling of energetic electron precipitation 241
rent status of the modeling efforts has been demonstrated
with regard to electron precipitation bursts during a mod-
erate substorm condition on 12 April 2014 (Kp= 5, min.
DST=−80 nT, min. AL=−700 nT). Signal amplitude dis-
turbances along a 37.5 kHz radio propagation path from Ice-
land (63.9◦ N, 22.5◦W) to a midlatitude site (52◦ N, 8◦ E)
have been modeled successfully and an electron energy input
distribution function has been derived. Future work intends
to model many different precipitation events and to further
validate the parametrization of the electron input distribution
function. For this purpose our software has to be optimized
with regard to speed to allow for faster modeling cycles. The
space time characterization of electron energy spectra can
help to quantify the effectiveness of energetic electron pre-
cipitation with regard to NOx production and ozone deple-
tion at mesospheric heights, underlining the importance of
energetic electron precipitation as a part of solar influence
on the atmosphere and the climate system (Andersson et al.,
2014).
Acknowledgements. Swarm Level 2 data have been provided
by the European Space Agency and the POES/Metop data have
been provided by the US NOAA National Geophysical Data Center.
Edited by: M. Förster
Reviewed by: two anonymous referees
References
Andersson, M. E., Verronen, P. T., Rodger, C. J., Clilverd, M. A.,
and Seppaelae, A.: Missing driver in the SunEarth connection
from energetic electron precipitation impacts mesospheric ozone,
Nat. Comm., 5, 5197, doi:10.1038/ncomms6197, 2014.
Barth, C. A., Baker, D. N., Mankoff, K. D., and Bailey, S. M.: The
northern auroral region as observed in nitric oxide, Geophys.
Res. Lett., 8, 1463–1466, doi:10.1029/2000GL012649, 2001.
Brekke, A.: Physics of the upper polar atmosphere, John Wiley &
Sons, New York, USA, 1997.
Carson, B. R., Rodger, C. J., and Clilverd, M. A.: POES satellite
observations of EMIC-wave driven relativistic electron precipi-
tation during 1998–2010, J. Geophys. Res.-Space, 118, 232–243,
doi:10.1029/2012JA017998, 2012.
Clilverd, M. A., Seppaelae, A., Rodger, C. J., Thomson, N. R.,
Lichtenberger, J., and Steinbach, P.: Temporal variability of the
descent of high-altitude NOX inferred from ionospheric data, J.
Geophys. Res., 112, A09307, doi:10.1029/2006JA012085, 2007.
Cummer, S. A., Bell, T. F., and Inan, U. S.: VLF remote sensing of
the auroral electrojet, J. Geophys. Res., 101, 5381–5389, 1996.
Cummer, S. A., Inan, U. S., and Bell, T. F.: Ionospheric D region
remote sensing using VLF radio atmospherics, Radio Sci., 33,
1781–1792, doi:10.1029/98RS02381, 1998.
Fang, X., Randal, C. E., Lummerzheim, I. D., Solomon, S. C.,
Mills, M. J., Marsh, D. R., Jackman, C. H., Wang, W., and
Lu, G.: Electron impact ionization: A new parameterization for
100 eV to 1 MeV electrons, J. Geophys. Res., 113, A09311,
doi:10.1029/2008JA013384, 2008.
Ferguson, J. A.: Computer Programs for Assessments of Long-
Wavelength Radio Communications, Version 2.0, Technical Doc-
ument, SPAWAR Systems Center, San Diego, USA, available at:
http://www.dtic.mil/dtic/tr/fulltext/u2/a350375.pdf (last access:
12 May 2015), 1998.
Glukhov, V. S., Pasko, V. P., and Inan, U. S.: Relaxation of
transient lower ionospheric disturbances caused by lightning-
whistler-induced electron precipitation bursts, J. Geophys. Res.,
97, 16971–16979, 1992.
Mitra, A. P. and Rowe, J. N.: Ionospheric effects of solar flares – VI.
Changes in D-region ion chemistry during solar flares, J. Atmos.
Sol.-Terr. Phy., 34, 795–806, 1972.
Mitra, A. P.: D-region in disturbed conditions, including flares and
energetic particles, J. Atmos. Sol.-Terr. Phy., 37, 895–913, 1975.
Nicolet, M. and Aikin, A. C.: The Formation of the D Region of the
Ionosphere, J. Geophys. Res., 65, 1469–1483, 1960.
Ohtani, S., Wing, S., Newell, P. T., and Higuchi, T.: Lo-
cations of nights’ side precipitation boundaries relative to
R2 and R1 currents, J. Geophys. Res., 115, A10233,
doi:10.1029/2010JA015444, 2010.
Ritter, P., Lühr, H., and Rauberg, J.: Determining field-aligned cur-
rents with the Swarm constellation mission, Earth Planets Space,
65, 1285–1294, 2013.
Rodger, C. J., Molchanov, O. A., and Thomson, N. R.: Relaxation
of transient ionization in the lower ionosphere, J. Geophys. Res.,
103, 6969–6975, 1998.
Rodger, C. R., Clilverd, M. A., Thomson, N. R., Gamble, R. J., Sep-
paelae, A., Turunen, E., Meredith, N. P., Parrot, M., Sauvaud, J.
A., Berthelier, J. J.: Radiation belt electron precipitation into the
atmosphere: Recovery from a geomagnetic storm, J. Geophys.
Res., 112, A11307, doi:10.1029/2007JA012383, 2007.
Saetre, C., Stadsnes, J., Nesse, H., Aksnes, A., Petrinec, S. M.,
Barth, C. A., Baker, D. N., Vondrak, R. R., and Ostgaard, N.: En-
ergetic electron precipitation and the NO abundance in the upper
atmosphere: A direct comparison during a geomagnetic storm, J.
Geophys. Res., 109, A09302, doi:10.1029/2004JA010485, 2004.
Salmi, S.-M., Verronen, P. T., Thölix, L., Kyrölä, E., Backman, L.,
Karpechko, A. Yu., and Seppälä, A.: Mesosphere-to-stratosphere
descent of odd nitrogen in February-March 2009 after sudden
stratospheric warming, Atmos. Chem. Phys., 11, 4645–4655,
doi:10.5194/acp-11-4645-2011, 2011.
Semeniuk, K., McConnell, J. C. , Jin, J. J. Jarosz, J. R., Boone,
C. D., and Bernath, P. F.: N2O production by high energy au-
roral electron precipitation, J. Geophys. Res., 113, D16302,
doi:10.1029/2007JD009690, 2008.
Schmitter, E. D.: Remote auroral activity detection and modeling
using low frequency transmitter signal reception at a midlati-
tude site, Ann. Geophys., 28, 1807–1811, doi:10.5194/angeo-28-
1807-2010, 2010.
Schmitter, E. D.: Remote sensing planetary waves in the midlatitude
mesosphere using low frequency transmitter signals, Ann. Geo-
phys., 29, 1287–1293, doi:10.5194/angeo-29-1287-2011, 2011.
Schmitter, E. D.: Data analysis of low frequency transmitter signals
received at a midlatitude site with regard to planetary wave activ-
ity, Adv. Radio Sci., 10, 279–284, doi:10.5194/ars-10-279-2012,
2012.
Schmitter, E. D.: Modeling solar flare induced lower ionosphere
changes using VLF/LF transmitter amplitude and phase ob-
www.adv-radio-sci.net/13/233/2015/ Adv. Radio Sci., 13, 233–242, 2015
242 E. D. Schmitter: Remote sensing and modeling of energetic electron precipitation
servations at a midlatitude site, Ann. Geophys., 31, 765–773,
doi:10.5194/angeo-31-765-2013, 2013.
Schmitter, E. D.: Remote sensing and modeling of lightning
caused long recovery events within the lower ionosphere using
VLF/LF radio wave propagation, Adv. Radio Sci., 12, 241-250,
doi:10.5194/ars-12-241-2014, 2014.
Sigernes, F., Dyrland, M., Brekke, P., Chernouss, S., Lorentzen,
D. A., Oksavik, K., and Deehr, C. S.: Two methods
to forecast auroral displays, J. Space Weather, 1, A03,
doi:10.1051/swsc/2011003, 2011.
Thorne, R. M.: A cause of dayside relativistic electron possible
precipitation events, J. Atmos. Sol.-Terr. Phy., 36, 635–645,
doi:10.1016/0021-9169(74)90087-7, 1974.
Thorne, R. M., Li, W., Ni, B., Ma, Q., Bortnik, J., Chen, L., Baker,
D. N., Spence, H. E., Reeves, G. D., Henderson, M. G., Kletzing,
C. A., Kurth, W. S., Hospodarsky, G. B., Blake, J. B., Fennell, J.
F., Claudepierre, S. G., and Kanekal, S. G.: Rapid local accel-
eration of relativistic radiation-belt electrons by magnetospheric
chorus, Nature, 504, 411–414, doi:10.1038/nature12889, 2013.
Torkar, K. and Friedrich, M.: Tests of an Ion-Chemical Model of
the D- and Lower E-Region, J. Atmos. Terr. Phys., 45, 369–385,
1983.
Verronen, P. T., Turunen, E., Ulich, T., and Kyrola, E.: Modelling
the effects of the October 1989 solar proton event on mesospheric
odd nitrogen using a detailed ion and neutral chemistry model,
Ann. Geophys., 20, 1967–1976, 2002,
http://www.ann-geophys.net/20/1967/2002/.
Wait, J. R. and Spies, K. P.: Characteristics of the Earth-
ionosphere waveguide for VLF radio waves, NBS Tech.
Note 300, available at: http://nova.stanford.edu/~vlf/IHY_Test/
Tutorials/SfericsAndTweaks/Papers/Wait1964f.pdf (last access:
12 May 2015), 1964.
Adv. Radio Sci., 13, 233–242, 2015 www.adv-radio-sci.net/13/233/2015/